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New Second-Order Tangent Epiderivatives and Applications to Set-Valued Optimization

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Abstract

A new second-order tangent set is introduced, with which a new second-order tangent epiderivative is also introduced for a set-valued map. Applying a separation theorem for convex sets, second-order Fritz John and Kuhn–Tucker necessary optimality conditions are obtained for a point pair to be a weak minimizer of set-valued optimization problem. Under the assumption of lower semicontinuous, a second-order Kuhn–Tucker sufficient optimality condition is obtained for a point pair to be a weak minimizer of set-valued optimization problem.

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Acknowledgments

The authors are grateful to the anonymous referees for valuable and detail comments and suggestions which improved the paper. This research was supported by the National Natural Science Foundation of China Grant 11461044, the Natural Science Foundation of Jiangxi Province (20151BAB201027) and the Science and Technology Foundation of the Education Department of Jiangxi Province(GJJ12010).

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  1. Department of Mathematics, Nanchang University, Nanchang, 330031, China

    Zhenhua Peng & Yihong Xu

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  1. Zhenhua Peng
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  2. Yihong Xu
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Correspondence to Yihong Xu.

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Peng, Z., Xu, Y. New Second-Order Tangent Epiderivatives and Applications to Set-Valued Optimization. J Optim Theory Appl 172, 128–140 (2017). https://doi.org/10.1007/s10957-016-1011-1

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  • DOI: https://doi.org/10.1007/s10957-016-1011-1

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